SOLUTION: The length of an altitude of an equilateral triangle is 15cm. Find the perimeter of the equilateral triangle.

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Question 426568: The length of an altitude of an equilateral triangle is 15cm. Find the perimeter of the equilateral triangle.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution: Denote x cm the side of equilateral triangle. The altitude of equilateral triangle divide the opposite side in two equal parts x/2 cm each.
Using Pythagorean theorem we write:
+x%5E2-15%5E2=%28x%2F2%29%5E2

4x%5E2-900=x%5E2
3x%5E2=900
x%5E2=300
x=sqrt(300) => x=10sqrt%283%29 cm
The perimeter is 3%2A10%2Asqrt%283%29=
30sqrt%283%29 cm.